algorithmic modeling for Rhino
edit 29/04/14 - Here is a new collection of more than 80 example files, organized by category:
This zip is the most up to date collection of examples at the moment, and collects together a wide variety of definitions made for various workshops and in response to forum questions. Thanks to all workshop attendees and forum members for your valuable input.
It is possible I've missed a few useful ones. If there is something else you'd like to see included please let me know
The examples below are mostly older, but I will leave them here for now until I am certain all the same topics are adequately covered in the 'official' collection above.
The wind component acts on sets of 3 points (typically each the vertices of each face of a triangulated mesh). It applies a force to each vertex, proportional to its area multiplied by the projection of the wind velocity vector onto the triangle normal.
CurvePull - Pulls particles onto a curve. This can be either a hard or soft constraint. Useful for fixing the boundary curves of tensile surfaces, yet allowing the nodes to slide along that boundary.
Align Pulls two line segments towards being parallel.
Planarity measures how planar a quad defined by 4 points is (it returns the shortest distance between the two diagonals).
Equalize adjusts a set of lines towards having equal length (it finds their average length, then treats each line as a spring with this as the rest the length). This demo shows how it can be used to make a quadrilateral circular (the 4 vertices lie on a common circle). Meshes made up of circular quads have a constant distance vertex-vertex offset mesh. (see http://www.dmg.tuwien.ac.at/pottmann/2008/pw_focal_07/pw_focal_07.html)
Laplacian acts on a central vertex, and its ring of neighbouring vertices. It finds the average position of the neighbours, and moves the central vertex towards this point. It also divides the same force up between the number of neighbours, reverses it and applies it to each of them. When applied to each vertex/set of surrounding neighbours of a mesh, this smooths it.
Shear pulls a particle towards the plane normal to a given line (or to a given height above that plane). It could be useful for example if you wanted to restrict some of the vertices of a mesh to match a plane for glazing lines, or in self-organizing particle systems if you want them to form surfaces not just clusters.
(also requires WeaverBird)
This demo shows how several forces can be combined to optimize different properties of a mesh. Sliders control the relative strengths of the Laplacian smoothing and Planarization forces.
A shear component keeps the base vertices on the ground plane but allows them to move around on it (Using the shear component here is quicker than constraining to a mesh).
The colours display how planar each quad of the mesh is.
It can sometimes be effective to use high smoothing/low planarization values to begin with and get a nice smooth form, then lower the smoothing and raise the planarization for the fine adjustments to get it within manufacturing tolerances.
Equilateralization - This shows how equalization of mesh triangle edge lengths can be combined with smoothing to create a pseudo-physical material that reacts to manipulation of the anchor points
This shows how the Hinge force can be used to keep the angle between faces of a mesh at a particular angle.
This takes a flat mesh, and a choice of which lines will be valley folds, and which ones mountain folds, and folds it into 3d. (Inspired by Tomohiro Tachi's rigid origami simulator)
Shows how to use solids (Breps or Meshes) as collision volumes and drape a simple fabric over them
You can also download an earlier collection of example files here:
(some of these may need slight changes and updating - I'll be trying to go through these over the next few days and make sure they are all compatible with the latest version. Also - many of them also require the WeaverBird plugin)
There is also a collection of links to further example files and helpful discussions here:
update: here's another example for the vortex force:
more example files to follow soon...